This parliament has had 48 months since first gathering in mid-May 2010 to sort out the arrangements for the next coalition. So why is it that the MP tasked with overseeing our constitutional arrangements is now demanding a change of plan?

Graham Allen, chair of the political and constitutional reform committee, hasn't been particularly happy with the debate about what exactly happens when the voters return a hung parliament. His team of MPs united to renew their criticisms of the Cabinet manual 'rule-book' earlier this year, warning much more needs to be done to boost public awareness - and get clearer rules, too. Now he has emailed out fresh concerns.

"If the result of the May 7th general election is not clear cut, the days immediately after it should not be characterised by a private fix by the party leaders, where newly elected members of parliament and their parties are bypassed," Allen says. This is exactly what happened in 2010, of course, when the Conservative-Lib Dem coalition was formed before parliament was recalled. Allen wants an alternative approach this time round.

"The royal proclamation can be issued as early as March 30th," he continues. "If it repeats the precedent of 2010 it would not convene MPs in parliament until May 19th. This would be 12 days after the election, by which time deals will have been done, manifestos compromised, and patronage promised."

The party leaders want to preserve this 12-day period for manoeuvring and negotiation; putting MPs in the position of voting on a new government would create a pressured situation in which backbenchers would be empowered at the expense of the leaders. It is unthinkable. But Allen believes it might just work.

So he's calling for parliament to be summoned to meet on Saturday May 9th, just two days after polling day. This would "debate and confirm any proposed arrangements for the composition and programme of the new government", he suggests.

The Saturday after the election on May 10th was a day of uncertainty and excitement. Behind closed doors frenzied talks were taking place, but it would take another three days before an agreement was reached. And that was in a scenario where there was, arithmetically speaking, only one feasible option for a stable coalition. In 2015, it might take much longer.

But Allen insists: "Deferring proper democratic scrutiny of any coalition deal-making particularly in the Queen's name should be avoided. Once parliament is dissolved, it is Her Majesty who issues a proclamation summoning the first meeting of the new parliament. This matter has to be resolved now before the dissolution since once the proclamation of the date of summoning the new parliament has been issued, it appears that the date of parliament's first meeting cannot be brought forward."

With a hung parliament now viewed as the most likely outcome of the election, Allen's comments aren't just dry theory any more. But with 47 months of this parliament past and one to go, the debate about what constitutes the rules of the game really should have been settled by now.

Back in 2010, before New Labour's final Budget, Vince Cable presented journalists with two graphs. One showed the Conservatives' anticipated approach to fixing the deficit: a rapid, and potentially painful, fiscal consolidation that looked rather unpleasant. The other showed Labour's alternative - slower, and therefore not so grim, but possibly less credible with the markets. At the time Cable, then the Liberal Democrats' Treasury spokesperson, held an essential agnostic position: his party would plump for something vague in the middle, he suggested.

Actually, they didn't. Going into government with David Cameron and George Osborne meant signing up to the Tories' more brutal approach to austerity. The Lib Dems have been complicit in adopting the rushed kind of cuts driven by the Conservatives' ideology. When contrasted with Cable's now-forgotten indifference, this is in some ways an even bigger broken promise than tuition fees. Which is why, five years down the line, we have to treat the Lib Dems' approach to the deficit for 2015-20 with some suspicion.

Today the party is outlining its plans in some detail. It is well ahead of the other parties in making clear its intentions. And these very specific proposals are unrecognisable from the vague suggestions offered by Cable in early 2010. Now the Lib Dems have a very clear plan, and they want you to pay attention.

More of us are sitting up and taking notes, it's true, because we know there is a strong chance the party's plans will feature in the coalition negotiations. They got the income tax threshold raised, whatever the Tories may now say to take credit for it. And the Lib Dems are already in government, so they are starting from a clearly established position, not making up policy on the hoof. It gives them more attention, but it also hobbles them.

The problem for Nick Clegg is his hands are tied by the last government. When the deputy prime minister says the plan is to "finish the job", he fails to accept any responsibility for not getting the job done on time in the first place. By now the electorate should have been basking in a recovering economy. The indicators may be improving, but voters haven't noticed it just yet. This is unlikely to make them very receptive to accepting the need for more austerity - as the Lib Dems and Conservatives have been forced to - by offering joint spending plans to 2017/18.

On the campaign trail in 2010

The result is an offering today which will not win over many voters. The Liberals calculate they need to come up with another £30 billion of cuts. They have ideas about how to achieve this, too: a whopping big banking levy (because the City is just as much to blame now for the crash as it was in 2008), stripping wealthy pensioners of payouts like free TV licences, and finally pushing through the much-vaunted mansion tax. They'll need more, but that's a decent start.

Yet already they've identified a long list of people who are now set to lose out. So to boost their 'we're doing this fairly' credentials, the proposal is to tweak the spending cuts / tax rises ration from 80:20 to something like 75:25. This is something the Tories have shied away from, because any kind of tax hike is in their view electorally toxic. The Lib Dems seem to think they can batter suspicious voters into agreement by explaining how reasonable they're being.

Quibbling over the balance of cuts when the job was supposed to have been finished by now anyway does not look much like bread and honey. And unfortunately, because these cuts will immediately follow the election, they will dominate the headlines. The much vaguer plans for what the party would do after 2017/18 simply can't compete.

In a growing economy, aides to Clegg say, the Lib Dem instinct is to start restoring public spending levels wherever possible. That is nice. It is like saying to a man who's just had his leg chopped off that the intention is very much to glue his knee back on in several years' time. Surely this is not going to go down well on the doorstep.

But this is what Lib Dem campaigners are being given to work with. It must be especially galling for them because, after years of a Lib Dem wipeout being the universally expected outcome of their adventure in government, commentators have finally begun suggesting they could keep most of their seats. Achieving that needs more than just the incumbency factor - but the proposals outlined today aren't going to add much.

"When balancing the books, we will stay the course - it is for other parties to lurch left and right," Danny Alexander says. How reassuring to the markets - and how unattractive to many voters - his promise will be.

One thing the party has shied away from promoting is its preference for shifting the balance of austerity from spending cuts to tax rises. What is revealing here is how this has been presented. Instead of declaring the £30 billion of cuts still to come should be 60:40 on cuts/tax hikes, the Lib Dems have instead suggested the total cuts package from 2010 onwards will shift from 80:20 to 75:25.

This isn't much of a difference, really – but highlighting 60:40 is really distinctive and, actually, is by far the most interesting point to emerge from today's announcement. Why wasn't it placed front and centre? It suggests the party is pulling its punches against the Conservatives – but maybe activists can embrace the hidden meaning of the figures and point out that the Lib Dems are becoming the party of tax rises. Even if their politicians are wary of admitting it.

It was an extraordinary gamble for a parliament shamed by the expenses scandal – so has letting the TV cameras into the Commons left MPs looking even worse than they did before?

Michael Cockerell and his team of cameramen have been omnipresent for the last year or so. The level of access they've had is unprecedented, because the Commons has always been touchy about any kind of scrutiny. When I made a documentary for BBC Radio 4 last year the rigmarole of getting permission to record in the main building – which, as officials pointed out, is still a royal palace – was truly astonishing. So it's no surprise to learn it took Cockerell six years to get the green light for this project.

The officials running parliament said 'yes' because they're determined to show the Commons is changing. They may work in a crumbling, Victorian mock Gothic Palace – and many of its important people wear what look like something out of a Harry Potter movie – but they are up-to-date, honest.

This week's episode portrayed parliament for what it is: its reputation as battered as the fabric of the building is in tatters. Some MPs, like the likeable stars Sarah Champion and Charlotte Leslie, are all for shaking up the fusty traditions that make parliament what it is; others seem like living embodiments of Westminster's antiquated way of doing things. It is in revealing the Commons' most enduring habits that Cockerell comes closest to making parliament look bad.

Here's a few of the most misleading parts of the programme that some in the Palace might feel were a bit harsh:

Sir Robert Rogers taking snuff outside the Commons chamber and declaring "my goodness, that's invigorating!" This is a centuries-old tradition that Sir Robert has long highlighted as one of the idiosyncrasies of his job. Putting it in the programme's intro was attention-grabbing, but also cringeworthy.

Labour MP Steve Rotherham complaining about people in parliament being rude when he held open doors for others. "Not one of them said 'ta, thanks very much'," he moaned. This is simply not true. Everyone in parliament is polite – just like everywhere else.

Conservative MP Andrew Percy isn't impressed with the geographical partisanship of the members' tea room. "When I first came here I sat in the wrong place," he says. "Somebody said 'that's a Labour table'. And I thought, there's all these old traditions. You go in a coffee shop and you sit where you want, don't you'?" Is this something to whinge about? Or isn't it just like any sixth form common room, where people sit in the same place?

These minor glitches are as nothing to the series' overarching narrative, though. This was hinted at in the story of the clerk, Sir Robert Rogers. Episode one finishes with the moving applause given to Sir Robert by MPs when Speaker John Bercow – who was virtually absent from the programme – confirmed to the Commons his plan to take early retirement.

We all know what followed: a botched recruitment process to find a new clerk that left Bercow damaged and abashed. How Cockerell treats the story of MPs' revolt against the Speaker's plans to split Sir Robert's job into two will have a real impact on the public's perception of parliament.

The Speaker, having watched last night's programme, must have felt qualms about how this story would play out in the three remaining episodes. It is entirely possible that, when viewed in its entirely, Inside The Commons will reveal our parliament to be a nobler, better place than many of the public thought it to be – while Bercow will end up looking diminished.

Only the Tories stand in the way of a constitutional convention. If a vote were held in the Commons on this issue, there is a strong chance it would be approved. So is a petition of just 15,000 signatures really the best way of underlining its importance?